Question

Can someone walk me through this problem! I have been stuck on it! I WILL MEDAL!!

Answer 1

were you able to graph this system?

Answer 2

Not yet, Give me a sec!

Answer 3

alright

Answer 4

alternatively you can check which ordered pair works

Answer 5

Do I graph x > - 2 or the one under it?

Answer 6

you graph them both on the same xy coordinate grid

Answer 7

what does x > -2 look like?

Answer 8

The graph looks like this

Answer 9

very good, now how about the other inequality

Answer 10

Like this

Answer 11

ok imagine them both plotted together

what does the overlapping region look like?

Answer 12

It would be (-2, -3.5)

Answer 13

are you able to see what the overlapping region looks like?

Answer 14

it might help to start with the second inequality you posted, then shade out x > -2 on top of it

Answer 15

I am supposed to be checking each choice for the correct answer by switching the x,y with the choices?

Answer 16

yes that's another way to check

Answer 17

for example, let's focus on just choice A for now

that is (x,y) = (-3,-1)

since x = -3 and y = -1 we can plug them into each inequality

x > -2
-3 > -2 ... replaced x with -3

-3 > -2 is FALSE, so (-3,-1) is NOT a solution to the system

Answer 18

you need to see which point makes both inequalities true

Answer 19

Okay. so (-1, 6)

-1>-2 is not false

6 ≤ 2(-1) +7
6 ≤ 5 There is no solution to that..

^^Is that how I can check it? @jim_thompson5910

Answer 20

your work looks good

since 6 ≤ 5 is false, that means (-1,6) is also not a solution. So move onto the next answer choice

Answer 21

Next; (-1, 4)
-1>-2 is not false

4 ≤ 2(4) +7 Many Solutions

Answer 22

What do we do when it has many Solutions @jim_thompson5910

Answer 23

4 ≤ 2(4) +7 simplifies to 4 ≤ 15 which is true

since both inequalities are true, this means (-1,4) is a solution

now check choice D

Answer 24

wait a second

Answer 25

you plugged in the wrong x value

Answer 26

4 ≤ 2(4) +7 should be 4 ≤ 2(-1) +7

notice how x is -1

Answer 27

Yes, that would equal to 4 ≤ 5

Answer 28

that's also true, so (-1,4) is still a solution

Answer 29

(1,11)

1> -2 Many solutions


11 ≤ 2(11) +7 Many solutions

Answer 30

in the second inequality, you replaced x with the wrong x value

Answer 31

What should it be replaced with?

Answer 32

with 1 since the first number of (1,11) is 1

Answer 33

11 ≤ 2(1) +7 no solution

Answer 34

yes since the right side turns into 9 which is NOT greater than 11

Answer 35

or equal to it

Answer 36

so D is not a solution

Answer 37

C (-1, 4) was the only solution, which means it's correct?

Answer 38

here's a visual way to look at it

See the attached image for the graph of the inequalities and the points plotted.

The only point in the red solution region is point C. The other points are outside of the solution region. So only (-1,4) is the solution.

Answer 39

yes only C is the solution

Answer 40

Wow. That actually made so much sense. :P
Thank you so much for the help!

Answer 41

no problem

Answer 42

Do mind check the 4 other after I am done solving them?

Answer 43

checking*

Answer 44

sure I can help out with that

Answer 45

Is this an easier way to figure it out, or do I have to check each problem like before?

Answer 46

looks great. That's the only point in both shaded regions...aka the final shaded solution region

Answer 47

the other points are in the red shaded region, but NOT in the blue shaded region. They would need to be in both

Answer 48

Okay! Awesome!

You wouldn't belive how much trouble I have been having with this. Thank you so much!

Answer 49

I'm glad it's making more sense now